Three concentric spherical shells have radii a,b and `c(a lt b lt c)` and have surface charge densities `sigma, - sigma` and `sigma` respectively. If `V_(A),v_(B)` and `V_(c)` denote the potentials of the three shells, then, for `V_(A) = V_(C)`, we get-

Options

A. `c = (a+b)/(2)`
B. `c= b-a`
C. `c=2(a+b)`
D. `c= a+b`

Answer

D

Explanation

`V_(A) = k [(q_(A))/(a)+(q_(B))/(b)+(q_(c))/(c_(r))]`
`= (1)/(4pi in_(0)) ((sigma 4pia^(2))/(a)+(-sigma4pi b^(2))/(b)+(sigma4pic^(2))/(c))`
`=(sigma)/(in_(0)) [a-b+c]`
`V_(c) = k [(q_(A))/(c)+(q_(B))/(c)+(q_(c))/(c)]`
`= (1)/(4pi in_(0)) [(sigma 4pia^(2))/(c)+(sigma4pib^(2))/(c)+(sigma4pic^(2))/(c)]`
`= sigma [(a^(2)-b^(2)+c^(2))/(c)]`
`V_(A) = V_(C)`
`(sigma)/(in_(0)) (a-b+c) =(sigma)/(in_(0)) ((a^(2)-b^(2))/(c)+c)`